Philosophy - five equivalence rules

The next assignment is available for you to begin. It corresponds to material from Chapter 8, section 2 and VLecture 12. You will now be performing proofs using the first five equivalence rules, in addition to the eight implicational rules we learned in the last section.

You may complete this assignment with either Canvas text entry or by copying and pasting it into your word processing software and submitting it as a MSWord or Adobe document.

 

Directions: Complete the following proofs below using any of the 8 implicational rules and first five equivalence rules. (as found in the inside cover of the text as well as chapter 8, sections 1 and 2.) You may print, write in answers, and then scan or take photos. You may also use your word processing software. Feel free to use the following key for copying and pasting the logical operators and conclusion indicator.

Negation: ~

Conjunction: ⦁

Disjunction: ⌵

Conditional: →

Biconditional: ↔ 

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Conclusion: ∴

1. 1. P ⌵~~Q

          ∴ Q ⌵ P

 

 

 

2. 1.~(E ⌵T)

         ∴ ~T

 

 

 

3.   1. ~P   2. ~Q   ∴ ~(P ⌵ Q)

 

 

 

4.   1. [(A → B) ⌵ C] ⦁ ~C

    ∴ ~B → ~A

 

 

 

5. 1. ~T ⦁ (R ⦁ ~~Q)  ∴ (R ⦁ ~T) ⦁ Q

 

 

 

 

6.  1. (P → Q) ⦁ (Q → R)   ∴ (~R → ~P) ⌵ S